Decentralized Drone Swarm Coordination via Broadcast-as-Shared-State and Hierarchical PCA-Tree Bisection

A four-layer decentralized coordination architecture for drone swarms built on a single primitive: broadcast-as-shared-state with locally- deterministic per-drone computation against a PCA tree of the target manifold. The four layers (assignment, recovery, priority allocation, localization) are independently provable, empirically validated across N=10 to N=10,000, and compose without interference. Witness-alarm byzantine detection via mutual physical observation provides primary adversarial defense. Includes formal proofs (slot-disjointness lemma, three-part composition theorem, rounding O(1/sqrt(N)) bound), bootstrap-CI empirical validation across all headline numbers, a CBBA reference implementation showing 14x messaging advantage at N=100, and v1.3 underwater feasibility benches for acoustic detection-map gossip, link budget/capacity accounting, and vertical acoustic relay localization.